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A company produces tables which are packed in batches of 100. An analysis of the defective tubes in different batches has received the following information: No. of defective tubes Less than 5 5 – 9 - Mathematics and Statistics

Sum

A company produces tables which are packed in batches of 100. An analysis of the defective tubes in different batches has received the following information:

No. of defective tubes Less than 5 5 – 9 10 – 14 15 – 9 20 – 24 25 – 29 30 and above
No. of tubes 45 51 84 39 20 8 4

Estimate the number of defective tubes in the central batch.

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Solution

To find the number of defective tubes in the central batch, we have to find Q2.
Since, the given data is not continuous, we have to convert it in the continuous form by subtracting 0.5 from the lower limit and adding 0.5 to the upper limit of every class interval.
∴ the class intervals will be
Less than 4.5, 4.5 – 9.5, etc.
We construct the less than cumulative frequency table as given below:

No. of defective tubes No. of tubes
(f)
Less than cumulative frequency
(c.f.)
Less than 4.5 45 45
4.5 – 9.5 51 96
9.5 – 14.5 84 180 ← Q2
14.5 – 19.5 39 219
19.5 – 24.5 20 239
24.5 – 29.5 8 247
29.5 and above 4 251
Total 251  

Here, N = 251
Q2 class = class containing `((2"N")/4)^"th"` observation

∴ `(2"N")/4=(2xx251)/4` = 125.5

Cumulative frequency which is just greater than (or equal to) 125.5 is 180.
∴ Q2 lies in the class 9.5 – 14.5
∴ L = 9.5, h = 5, f = 84, c.f. = 96

∴ Q2 = `"L" "h"/"f"((2"N")/4-"c.f.")`

= `9.5 + 5/84 (125.5 - 96)`

= `9.5 + 5/84 xx 29.5`

= `9.5 + (147.5)/84`

= 9.5 + 1.76
= 11.26

Concept: Partition Values
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APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 1 Partition Values
Miscellaneous Exercise 1 | Q 14 | Page 22
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